What kind of wound would cause the slowest yet surely inevitable death in the middle ages?

Bacterial infection. Any minor injury that leads to an infection and is left untreated, particularly on the torso, or head. This actually persists into the mid-modern era, and it’s only, really, modern antibiotics and an understanding of the need to protect wounds against bacteria that have finally moved this out of the fatal and into the treatable range.

European medicine in the middle ages looks more like creative torture to a modern observer. But, if you don’t outright kill someone, humans are ridiculously hearty and can survive trauma that will flat out kill nearly any other animal on the planet, even without medical attention. This means killing someone with a non-lethal wound is surprisingly hard.

The examples that still apply tend to be things like rupturing internal organs (like the kidneys or liver), which will kill you, but the blood loss will take awhile.